Recent Answers

Currently available out of the box controls offer only standard dropdown list, checkboxes or radiobuttons for selection of the attribute product options used in product variants.
You are therefore limited to styling options for those controls, alternatively, some jQuery solutions or similar can be used to change the appearance of the controls significantly.

For more robust solution, you have about three options:
1) Write a custom control inspired by the ShoppingCartItemSelector.ascx, that will render the options using your custom code (pulling data about variants using API), outputting an exact markup you need. This may require quite a lot of implementation work, but it's probably the best option at the moment.

2) Keep variants as separate products with their own URLs and write custom variant selectors that can read those variant products and base the selectors on them. This won't benefit from the available Variants features and still requires some coding.

3) Wait for improved MVC solution support for E-Commerce features in the next Kentico version, where it will be fairly easy to create and use your own selection controls with good support from the API. This is actually not an option yet and you cannot influence when it will be available. You can think about it as a possibility during this year, but there are no specific dates known yet. I've mentioned this mainly to let you know that the options will get better.